Mathematics - Algebra

Choose one of the concepts for rational expressions that helps you to solve an equation with a rational expression. Explain this concept. My choice is ( writing rational expressions) . Attempt to explain this concept, tell why it is important when attempting to solve an equation with a rational expression, then give an example.

a) Use the accompanying graph to estimate the cost for removing 90% and 95% of the toxic chemicals.
b) Use the formula to find ........
(c) What happens to the cost as the percentage of pollutants removed approaches 100%?

Should algebra be taught to everyone? Who should study algebra? The statements below serve as possible answers to these questions and are only 'food for thought.' I welcome your constructive ideas and comments on one or several of them.
Whether you agree or do not agree, the study of algebra is good for the brain. The b

Solve the problem
5).
A school library has $15,000 to spend on new books among the four
categories of biology, chemistry, physics, and mathematics. If the amount spent on biology books is to be the same as the amount spent on chemistry books and if the amount spent on mathematics books is to be the same as the total spent

Suppose X is a measurable space, E belongs to the sigma algebra ( I believe to the sigma algebra in X) , let us consider X\E = Y. Show that all sets B which can be expressed as A\E, where A belongs to the sigma algebra in X, form a sigma-algebra in Y.
Please justify every step and claim you make in the solution.